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29 March 2024
 
  » arxiv » 1911.6374

 Article overview


Regularity conditions for spherically symmetric solutions of Einstein-nonlinear electrodynamics equations
Alberto A. Garcia-Diaz ; Gustavo Gutierrez-Cano ;
Date 14 Nov 2019
AbstractIn this report, for static spherically symmetric (SSS) solutions of the Einstein equations coupled to nonlinear electrodynamics (NLE) the regularity conditions at the center are established. The NLE is derived from a Lagrangian $mathcal{L}=mathcal{L}(mathcal{F})$, depending on the electromagnetic invariant $mathcal{F}=F_{mu u},F^{mu u}/4$. Regular solutions are characterized by the finite behavior at the center of the curvature invariants of the Riemman tensor. For regular SSS metrics, the traceless Ricci (TR) tensor eigenvalue $S$, the Weyl tensor eigenvalue $Psi_2$ and the scalar curvature $R$ are singular--free at the center. Regular NLE SSS electric solutions, which are characterized by the ${mathcal{F}}(r=0)=0$, approach to the flat or conformally flat de Sitter--Anti de Sitter (regular) spacetimes at the center; moreover, this family of solutions may exhibit different asymptotic behavior at spatial infinity such as the Reissner--Nordtr"om (Maxwell) asymptotic, or present the dS--AdS or other kind of asymptotic. Pure magnetic NLE SSS solutions shear the single magnetic invariant $2mathcal{F}_m= h_0^2/r^4$, thus they are singular in the magnetic field and may exhibit a regular flat or (A)dS behavior at the center.
Source arXiv, 1911.6374
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